Treffer: A multipole based treecode using spherical harmonics for potentials of the form r-λ

Title:
A multipole based treecode using spherical harmonics for potentials of the form r-λ
Authors:
SRINIVASAN, Kasthuri, MAHAWAR, Hemant, SARIN, Vivek
Source:
Computational science (Atlanta GA, 22-25 May 2005)Lecture notes in computer science. :107-114
Publisher Information:
Berlin: Springer, 2005.
Publication Year:
2005
Physical Description:
print, 12 ref 3
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Sciences exactes et technologie, Exact sciences and technology, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Algorithme rapide, Fast algorithm, Algoritmo rápido, Complexité algorithme, Algorithm complexity, Complejidad algoritmo, Coordonnée cartésienne, Cartesian coordinate, Coordenadas cartesianas, Harmonique sphérique, Spherical harmonic, Armónica esférica, Polynôme Legendre, Legendre polynomial, Polinomio Legendre, Borne erreur, Error bound, Limite error
Document Type:
Konferenz Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Department of Computer Science, Texas A&M University, College Station, TX, United States
ISSN:
0302-9743
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=16990952
Rights:
Copyright 2005 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Accession Number:
edscal.16990952
Database:
PASCAL Archive

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In this paper we describe an efficient algorithm for computing the potentials of the form r-λ where λ > 1. This treecode algorithm uses spherical harmonics to compute multipole coefficients that are used to evaluate these potentials. The key idea in this algorithm is the use of Gegenbauer polynomials to represent r-λ in a manner analogous to the use of Legendre polynomials for the expansion of the Coulomb potential r-1. We exploit the relationship between Gegenbauer and Legendre polynomials to come up with a natural generalization of the multipole expansion theorem used in the classical fast multipole algorithm [2]. This theorem is used with a hierarchical scheme to compute the potentials. The resulting algorithm has known error bounds and can be easily implemented with modification to the existing fast multipole algorithm. The complexity of the algorithm is O(p3N log N) and has several advantages over the existing Cartesian coordinates based expansion schemes.